Three dimensional strain measurement by a Bragg grating sensor subjected to axial and transverse load simultaneously
The objective of this thesis is to establish mathematical models for predicting strains in the axial and other two orthogonal (transverse) directions of a multi-parameter Bragg grating sensor which is subjected to an axial and transverse loadings simultaneously. Previous work by other researchers has established models for predicting axial strains, but not a combination of those three strain components. Test specimens consisted of polarization maintaining Bragg grating sensors created in optical fibers with bow-tie stress applying parts. Each of the sensors had two Bragg wavelength peaks at around 1300 nm, and two others around 1550 nm, and those four peaks moved due to external stimuli such as applied loads and/or temperature changes. The change in wavelength from a certain reference state, which is called a wavelength shift denoted by da,, was considered as the key to predict the strains due to the external stimuli experienced by the sensor. The specimens underwent thermal, axial, transverse, and combined loading tests, and the relations between the wavelength shifts and external stimuli were investigated. In order to predict the strains experienced by the sensor from the data of wavelength shifts obtained in the experiments, several mathematical models were investigated. Those mathematical models were categorized into linear and non-linear models. The linear model assumed a linear relation between the wavelength shifts and the loads applied, while the non-linear model tried to deal with more general conditions since a non-linear relation was observed in some of the data. The computed strains were compared with ones obtained from finite element analyses, and the accuracies of the mathematical models were studied. Some researchers hypothesize that the non-linearity between wavelength shifts and applied loads is caused by the rotation of optical axes of the sensor due to large transverse loads. The related studies were reviewed, and some computations were conducted to understand a possible cause for the non-linear behavior. If a multi-parameter sensor is properly embedded in a material, it is expected that one might be able to measure the multi-axial strains in the material from data on wavelength shifts. An example of an experiment that could check this possibility was formulated, and the related computational procedures were discussed. Also, to improve the ability of the multi-parameter sensor to determine transverse strains, some different cross-sectional geometries of an optical fiber sensor were suggested.